Sierpiński Fractals and the Dimension of Their Laplacian Spectrum-Reference-Cited by-同舟云学术

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Sierpiński Fractals and the Dimension of Their Laplacian Spectrum

Published:2023-05-17 Issue:3 Volume:28 Page:70
ISSN:2297-8747
Container-title:Mathematical and Computational Applications
language:en
Short-container-title:MCA

Author:

Pollicott Mark¹,Slipantschuk Julia¹

Affiliation:

1. Department of Mathematics, University of Warwick, Coventry CV4 7AL, UK

Abstract

We establish rigorous estimates for the Hausdorff dimension of the spectra of Laplacians associated with Sierpiński lattices and infinite Sierpiński gaskets and other post-critically finite self-similar sets.

Funder

ERC-Advanced

Publisher

MDPI AG

Subject

Applied Mathematics,Computational Mathematics,General Engineering

Link

https://www.mdpi.com/2297-8747/28/3/70/pdf

Reference32 articles.

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2. Kigami, J. (2008). Analysis on Fractals, Cambridge University Press. Cambridge Tracts in Mathematics 143.

3. Spectrum of harmonic excitations on fractals;Rammal;J. Phys.,1984

4. Laplace operators on fractal lattices with random blow-ups;Sabot;Potential Anal.,2004

5. On eigenvalue problems for Laplacians on p.c.f. self-similar sets;Shima;Jpn. J. Indust. Appl. Math.,1996

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